SciPost Physics

SciPost Phys. 10, 015 (2021) · published 25 January 2021

• doi: 10.21468/SciPostPhys.10.1.015
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles. As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations.

• Bulchandani et al., Superdiffusion in spin chains
  J. Stat. Mech. 2021, 084001 (2021) [Crossref]
• Bulmash et al., Multipole groups and fracton phenomena on arbitrary crystalline lattices
  SciPost Phys. 15, 235 (2023) [Crossref]
• Yoo et al., Open-system spin transport and operator weight dissipation in spin chains
  Phys. Rev. B 107, 115118 (2023) [Crossref]
• Delacrétaz et al., Nonlinear response in diffusive systems
  SciPost Phys. 16, 047 (2024) [Crossref]
• Stahl et al., Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
  SciPost Phys. 16, 068 (2024) [Crossref]
• Langlett et al., Noise-induced universal diffusive transport in fermionic chains
  Phys. Rev. B 108, L180303 (2023) [Crossref]
• Roy et al., Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
  Phys. Rev. B 107, L100413 (2023) [Crossref]
• Glorioso et al., Breakdown of hydrodynamics below four dimensions in a fracton fluid
  Nat. Phys. 18, 912 (2022) [Crossref]
• Stahl et al., Fracton superfluid hydrodynamics
  Phys. Rev. B 108, 144509 (2023) [Crossref]
• Schubert et al., Quantum versus classical dynamics in spin models: Chains, ladders, and square lattices
  Phys. Rev. B 104, 054415 (2021) [Crossref]
• McRoberts et al., Long-lived solitons and their signatures in the classical Heisenberg chain
  Phys. Rev. E 106, L062202 (2022) [Crossref]
• Morningstar et al., Hydrodynamics in long-range interacting systems with center-of-mass conservation
  Phys. Rev. B 108, L020304 (2023) [Crossref]
• De Nardis et al., Stability of Superdiffusion in Nearly Integrable Spin Chains
  Phys. Rev. Lett. 127, 057201 (2021) [Crossref]
• Glorioso et al., Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
  J. High Energ. Phys. 2023, 22 (2023) [Crossref]
• McRoberts et al., Anomalous dynamics and equilibration in the classical Heisenberg chain
  Phys. Rev. B 105, L100403 (2022) [Crossref]
• von Keyserlingk et al., Operator backflow and the classical simulation of quantum transport
  Phys. Rev. B 105, 245101 (2022) [Crossref]
• Bu et al., Holographic Schwinger-Keldysh field theory of SU(2) diffusion
  J. High Energ. Phys. 2022, 223 (2022) [Crossref]
• Gopalakrishnan et al., Anomalous transport from hot quasiparticles in interacting spin chains
  Rep. Prog. Phys. 86, 036502 (2023) [Crossref]
• Doyon, Hydrodynamic Projections and the Emergence of Linearised Euler Equations in One-Dimensional Isolated Systems
  Commun. Math. Phys. 391, 293 (2022) [Crossref]
• Žnidarič, Superdiffusive magnetization transport in the XX spin chain with nonlocal dephasing
  Phys. Rev. B 109, 075105 (2024) [Crossref]
• Majidy et al., Noncommuting conserved charges in quantum thermodynamics and beyond
  Nat Rev Phys 5, 689 (2023) [Crossref]
• Anakru et al., Non-Fermi liquids from dipolar symmetry breaking
  Phys. Rev. B 108, 165112 (2023) [Crossref]
• Qi et al., Hydrodynamics of higher-rank gauge theories
  SciPost Phys. 14, 029 (2023) [Crossref]
• Bertini et al., Finite-temperature transport in one-dimensional quantum lattice models
  Rev. Mod. Phys. 93, 025003 (2021) [Crossref]
• Bulchandani et al., Hydrodynamics of quantum spin liquids
  Phys. Rev. B 104, 235412 (2021) [Crossref]
• Žnidarič, Modified Matthiessen's rule: More scattering leads to less resistance
  Phys. Rev. B 105, 045140 (2022) [Crossref]
• Moudgalya et al., Spectral statistics in constrained many-body quantum chaotic systems
  Phys. Rev. Research 3, 023176 (2021) [Crossref]
• Huang et al., Hydrodynamic effective field theories with discrete rotational symmetry
  J. High Energ. Phys. 2022, 82 (2022) [Crossref]
• Claeys et al., Absence of Superdiffusion in Certain Random Spin Models
  Phys. Rev. Lett. 128, 246603 (2022) [Crossref]
• De Nardis et al., Nonlinear Fluctuating Hydrodynamics for Kardar-Parisi-Zhang Scaling in Isotropic Spin Chains
  Phys. Rev. Lett. 131, 197102 (2023) [Crossref]
• Gopalakrishnan et al., Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems
  Annu. Rev. Condens. Matter Phys. 15, 159 (2024) [Crossref]
• Winer et al., Spontaneous symmetry breaking, spectral statistics, and the ramp
  Phys. Rev. B 105, 104509 (2022) [Crossref]
• Stahl et al., Spontaneous breaking of multipole symmetries
  Phys. Rev. B 105, 155107 (2022) [Crossref]